On a class of algorithms for total approximation
type: Item
instance of: scholarly article
title: On a class of algorithms for total approximation
zbMATH Open document ID: 0582.65006
DOI: 10.1016/0021-9045(85)90047-4
published in: Journal of Approximation Theory
publication date: 1985-01-01T00:00:00Z
review text: Let A be a given \(m\times n\) matrix and let \(b\in {\mathbb{R}}^ n\) with \(m>n\) and define \(Z:=(A,b)\). The following total approximation problem is considered: Find \(v\in {\mathbb{R}}^{n+1}\) to minimize \(\| Zv\|_ p\) such that \(\| v'\|_ q=1\) where \(p+q=pq\) and v' is obtained from v by deleting the first k components (usually \(k=0)\). A class of algorithms is proposed and a local convergence analysis as well as a partial global convergence analysis for it are given.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 3932276
zbMATH Keywords: linear data fitting
zbMATH Keywords: total approximation problem
zbMATH Keywords: local convergence
zbMATH Keywords: global convergence
author: G. A. Watson
MaRDI profile type: Publication
full work available at URL: 0021-9045(85)90047-4
OpenAlex ID: W2092086025
cites work: An Analysis of the Total Least Squares Problem
cites work: An Analysis of the Total Approximation Problem in Separable Norms, and an Algorithm for the Total $l_1 $ Problem
cites work: Q4743653
cites work: Numerical Methods for Linear Orthogonal Lp Approximation
cites work: Q3681822
description: scientific article; zbMATH DE number 3932276